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TY - CHAP
TI - The ${\Phi ^4}$ Model
A2 - Rivasseau, Vincent
AB - The simplest interacting field theory is the theory of a one-component scalar bosonic field φ with quartic interaction$g{\varphi ^4}$(${\varphi ^3}$which is simpler looks unstable). In${\mathbb{R}^d}$it is called the$\varphi _d^4$model. For*d*= 1, 2, 3 the model is superrenormalizable and has been built by constructive field theory. For*d*= 4 it is renormalizable in perturbation theory. Although a constructive version may not exist [Aiz][Frö], it remains a valuable tool at least for a pedagogical introduction to renormalization theory.

Formally the Schwinger functions of the$\varphi _d^4$are the moments of the measure:

$dv = \frac{1} {Z}{e^{( - g/4!)\int {{\varphi ^4} - ({m^2}/2)\int {{\varphi ^2} - (a/2)} \int {({\partial _\mu }\varphi {\text{ }}{\partial ^u}\varphi )} } }}D\varphi $. (1.3.1)

*g*is

EP - 36
PB - Princeton University Press
PY - 1991
SN - null
SP - 23
T2 - From Perturbative to Constructive Renormalization
UR - http://www.jstor.org/stable/j.ctt7zv6ds.6
Y2 - 2020/09/29/
ER -